Properties

Label 6003.2.a.t.1.18
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.60427 q^{2} +0.573689 q^{4} -1.49095 q^{5} +2.64378 q^{7} -2.28819 q^{8} +O(q^{10})\) \(q+1.60427 q^{2} +0.573689 q^{4} -1.49095 q^{5} +2.64378 q^{7} -2.28819 q^{8} -2.39188 q^{10} +0.452028 q^{11} -4.89824 q^{13} +4.24134 q^{14} -4.81826 q^{16} +1.33628 q^{17} +4.58359 q^{19} -0.855340 q^{20} +0.725176 q^{22} +1.00000 q^{23} -2.77708 q^{25} -7.85811 q^{26} +1.51671 q^{28} +1.00000 q^{29} +3.84793 q^{31} -3.15342 q^{32} +2.14375 q^{34} -3.94174 q^{35} +5.27307 q^{37} +7.35332 q^{38} +3.41157 q^{40} -2.68885 q^{41} -10.1738 q^{43} +0.259324 q^{44} +1.60427 q^{46} +12.2984 q^{47} -0.0104188 q^{49} -4.45519 q^{50} -2.81007 q^{52} -9.46067 q^{53} -0.673950 q^{55} -6.04948 q^{56} +1.60427 q^{58} -5.58963 q^{59} -12.7333 q^{61} +6.17312 q^{62} +4.57758 q^{64} +7.30302 q^{65} -10.7367 q^{67} +0.766606 q^{68} -6.32362 q^{70} -5.99397 q^{71} -4.80854 q^{73} +8.45943 q^{74} +2.62955 q^{76} +1.19506 q^{77} -14.2832 q^{79} +7.18377 q^{80} -4.31365 q^{82} -2.48262 q^{83} -1.99232 q^{85} -16.3215 q^{86} -1.03433 q^{88} +1.82218 q^{89} -12.9499 q^{91} +0.573689 q^{92} +19.7301 q^{94} -6.83388 q^{95} +5.67663 q^{97} -0.0167146 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.60427 1.13439 0.567196 0.823583i \(-0.308028\pi\)
0.567196 + 0.823583i \(0.308028\pi\)
\(3\) 0 0
\(4\) 0.573689 0.286844
\(5\) −1.49095 −0.666772 −0.333386 0.942790i \(-0.608191\pi\)
−0.333386 + 0.942790i \(0.608191\pi\)
\(6\) 0 0
\(7\) 2.64378 0.999256 0.499628 0.866240i \(-0.333470\pi\)
0.499628 + 0.866240i \(0.333470\pi\)
\(8\) −2.28819 −0.808998
\(9\) 0 0
\(10\) −2.39188 −0.756380
\(11\) 0.452028 0.136292 0.0681458 0.997675i \(-0.478292\pi\)
0.0681458 + 0.997675i \(0.478292\pi\)
\(12\) 0 0
\(13\) −4.89824 −1.35853 −0.679264 0.733894i \(-0.737701\pi\)
−0.679264 + 0.733894i \(0.737701\pi\)
\(14\) 4.24134 1.13355
\(15\) 0 0
\(16\) −4.81826 −1.20456
\(17\) 1.33628 0.324094 0.162047 0.986783i \(-0.448190\pi\)
0.162047 + 0.986783i \(0.448190\pi\)
\(18\) 0 0
\(19\) 4.58359 1.05155 0.525773 0.850625i \(-0.323776\pi\)
0.525773 + 0.850625i \(0.323776\pi\)
\(20\) −0.855340 −0.191260
\(21\) 0 0
\(22\) 0.725176 0.154608
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −2.77708 −0.555415
\(26\) −7.85811 −1.54110
\(27\) 0 0
\(28\) 1.51671 0.286631
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 3.84793 0.691108 0.345554 0.938399i \(-0.387691\pi\)
0.345554 + 0.938399i \(0.387691\pi\)
\(32\) −3.15342 −0.557450
\(33\) 0 0
\(34\) 2.14375 0.367650
\(35\) −3.94174 −0.666275
\(36\) 0 0
\(37\) 5.27307 0.866887 0.433443 0.901181i \(-0.357298\pi\)
0.433443 + 0.901181i \(0.357298\pi\)
\(38\) 7.35332 1.19287
\(39\) 0 0
\(40\) 3.41157 0.539417
\(41\) −2.68885 −0.419928 −0.209964 0.977709i \(-0.567335\pi\)
−0.209964 + 0.977709i \(0.567335\pi\)
\(42\) 0 0
\(43\) −10.1738 −1.55149 −0.775745 0.631047i \(-0.782626\pi\)
−0.775745 + 0.631047i \(0.782626\pi\)
\(44\) 0.259324 0.0390945
\(45\) 0 0
\(46\) 1.60427 0.236537
\(47\) 12.2984 1.79391 0.896956 0.442119i \(-0.145773\pi\)
0.896956 + 0.442119i \(0.145773\pi\)
\(48\) 0 0
\(49\) −0.0104188 −0.00148840
\(50\) −4.45519 −0.630059
\(51\) 0 0
\(52\) −2.81007 −0.389686
\(53\) −9.46067 −1.29952 −0.649762 0.760138i \(-0.725131\pi\)
−0.649762 + 0.760138i \(0.725131\pi\)
\(54\) 0 0
\(55\) −0.673950 −0.0908754
\(56\) −6.04948 −0.808395
\(57\) 0 0
\(58\) 1.60427 0.210651
\(59\) −5.58963 −0.727708 −0.363854 0.931456i \(-0.618539\pi\)
−0.363854 + 0.931456i \(0.618539\pi\)
\(60\) 0 0
\(61\) −12.7333 −1.63033 −0.815164 0.579230i \(-0.803353\pi\)
−0.815164 + 0.579230i \(0.803353\pi\)
\(62\) 6.17312 0.783987
\(63\) 0 0
\(64\) 4.57758 0.572198
\(65\) 7.30302 0.905828
\(66\) 0 0
\(67\) −10.7367 −1.31170 −0.655851 0.754891i \(-0.727690\pi\)
−0.655851 + 0.754891i \(0.727690\pi\)
\(68\) 0.766606 0.0929647
\(69\) 0 0
\(70\) −6.32362 −0.755817
\(71\) −5.99397 −0.711353 −0.355677 0.934609i \(-0.615750\pi\)
−0.355677 + 0.934609i \(0.615750\pi\)
\(72\) 0 0
\(73\) −4.80854 −0.562797 −0.281398 0.959591i \(-0.590798\pi\)
−0.281398 + 0.959591i \(0.590798\pi\)
\(74\) 8.45943 0.983389
\(75\) 0 0
\(76\) 2.62955 0.301630
\(77\) 1.19506 0.136190
\(78\) 0 0
\(79\) −14.2832 −1.60698 −0.803490 0.595318i \(-0.797026\pi\)
−0.803490 + 0.595318i \(0.797026\pi\)
\(80\) 7.18377 0.803170
\(81\) 0 0
\(82\) −4.31365 −0.476363
\(83\) −2.48262 −0.272503 −0.136251 0.990674i \(-0.543505\pi\)
−0.136251 + 0.990674i \(0.543505\pi\)
\(84\) 0 0
\(85\) −1.99232 −0.216097
\(86\) −16.3215 −1.76000
\(87\) 0 0
\(88\) −1.03433 −0.110260
\(89\) 1.82218 0.193150 0.0965752 0.995326i \(-0.469211\pi\)
0.0965752 + 0.995326i \(0.469211\pi\)
\(90\) 0 0
\(91\) −12.9499 −1.35752
\(92\) 0.573689 0.0598112
\(93\) 0 0
\(94\) 19.7301 2.03500
\(95\) −6.83388 −0.701142
\(96\) 0 0
\(97\) 5.67663 0.576374 0.288187 0.957574i \(-0.406947\pi\)
0.288187 + 0.957574i \(0.406947\pi\)
\(98\) −0.0167146 −0.00168843
\(99\) 0 0
\(100\) −1.59318 −0.159318
\(101\) −13.5455 −1.34782 −0.673912 0.738811i \(-0.735387\pi\)
−0.673912 + 0.738811i \(0.735387\pi\)
\(102\) 0 0
\(103\) −11.7141 −1.15422 −0.577112 0.816665i \(-0.695820\pi\)
−0.577112 + 0.816665i \(0.695820\pi\)
\(104\) 11.2081 1.09905
\(105\) 0 0
\(106\) −15.1775 −1.47417
\(107\) 6.38608 0.617365 0.308683 0.951165i \(-0.400112\pi\)
0.308683 + 0.951165i \(0.400112\pi\)
\(108\) 0 0
\(109\) −10.6768 −1.02265 −0.511325 0.859387i \(-0.670845\pi\)
−0.511325 + 0.859387i \(0.670845\pi\)
\(110\) −1.08120 −0.103088
\(111\) 0 0
\(112\) −12.7384 −1.20367
\(113\) 16.7781 1.57835 0.789174 0.614170i \(-0.210509\pi\)
0.789174 + 0.614170i \(0.210509\pi\)
\(114\) 0 0
\(115\) −1.49095 −0.139032
\(116\) 0.573689 0.0532657
\(117\) 0 0
\(118\) −8.96729 −0.825506
\(119\) 3.53282 0.323853
\(120\) 0 0
\(121\) −10.7957 −0.981425
\(122\) −20.4276 −1.84943
\(123\) 0 0
\(124\) 2.20751 0.198241
\(125\) 11.5952 1.03711
\(126\) 0 0
\(127\) −13.4329 −1.19198 −0.595990 0.802992i \(-0.703240\pi\)
−0.595990 + 0.802992i \(0.703240\pi\)
\(128\) 13.6505 1.20655
\(129\) 0 0
\(130\) 11.7160 1.02756
\(131\) −14.2198 −1.24239 −0.621196 0.783655i \(-0.713353\pi\)
−0.621196 + 0.783655i \(0.713353\pi\)
\(132\) 0 0
\(133\) 12.1180 1.05076
\(134\) −17.2246 −1.48798
\(135\) 0 0
\(136\) −3.05765 −0.262192
\(137\) 10.7302 0.916740 0.458370 0.888762i \(-0.348434\pi\)
0.458370 + 0.888762i \(0.348434\pi\)
\(138\) 0 0
\(139\) 18.1469 1.53920 0.769598 0.638529i \(-0.220457\pi\)
0.769598 + 0.638529i \(0.220457\pi\)
\(140\) −2.26133 −0.191117
\(141\) 0 0
\(142\) −9.61596 −0.806953
\(143\) −2.21414 −0.185156
\(144\) 0 0
\(145\) −1.49095 −0.123816
\(146\) −7.71420 −0.638432
\(147\) 0 0
\(148\) 3.02510 0.248662
\(149\) −9.55513 −0.782787 −0.391394 0.920223i \(-0.628007\pi\)
−0.391394 + 0.920223i \(0.628007\pi\)
\(150\) 0 0
\(151\) 3.72077 0.302792 0.151396 0.988473i \(-0.451623\pi\)
0.151396 + 0.988473i \(0.451623\pi\)
\(152\) −10.4881 −0.850699
\(153\) 0 0
\(154\) 1.91721 0.154493
\(155\) −5.73705 −0.460811
\(156\) 0 0
\(157\) 9.77367 0.780024 0.390012 0.920810i \(-0.372471\pi\)
0.390012 + 0.920810i \(0.372471\pi\)
\(158\) −22.9141 −1.82294
\(159\) 0 0
\(160\) 4.70158 0.371692
\(161\) 2.64378 0.208359
\(162\) 0 0
\(163\) 10.0749 0.789128 0.394564 0.918869i \(-0.370896\pi\)
0.394564 + 0.918869i \(0.370896\pi\)
\(164\) −1.54256 −0.120454
\(165\) 0 0
\(166\) −3.98279 −0.309125
\(167\) 9.78226 0.756974 0.378487 0.925607i \(-0.376444\pi\)
0.378487 + 0.925607i \(0.376444\pi\)
\(168\) 0 0
\(169\) 10.9928 0.845597
\(170\) −3.19622 −0.245139
\(171\) 0 0
\(172\) −5.83659 −0.445036
\(173\) −0.699661 −0.0531942 −0.0265971 0.999646i \(-0.508467\pi\)
−0.0265971 + 0.999646i \(0.508467\pi\)
\(174\) 0 0
\(175\) −7.34199 −0.555002
\(176\) −2.17799 −0.164172
\(177\) 0 0
\(178\) 2.92327 0.219108
\(179\) 5.88690 0.440007 0.220004 0.975499i \(-0.429393\pi\)
0.220004 + 0.975499i \(0.429393\pi\)
\(180\) 0 0
\(181\) −8.06805 −0.599694 −0.299847 0.953987i \(-0.596936\pi\)
−0.299847 + 0.953987i \(0.596936\pi\)
\(182\) −20.7751 −1.53996
\(183\) 0 0
\(184\) −2.28819 −0.168688
\(185\) −7.86186 −0.578015
\(186\) 0 0
\(187\) 0.604034 0.0441714
\(188\) 7.05548 0.514574
\(189\) 0 0
\(190\) −10.9634 −0.795369
\(191\) −8.20237 −0.593503 −0.296751 0.954955i \(-0.595903\pi\)
−0.296751 + 0.954955i \(0.595903\pi\)
\(192\) 0 0
\(193\) 6.48762 0.466989 0.233495 0.972358i \(-0.424984\pi\)
0.233495 + 0.972358i \(0.424984\pi\)
\(194\) 9.10686 0.653834
\(195\) 0 0
\(196\) −0.00597716 −0.000426940 0
\(197\) −4.31234 −0.307241 −0.153621 0.988130i \(-0.549093\pi\)
−0.153621 + 0.988130i \(0.549093\pi\)
\(198\) 0 0
\(199\) −20.3079 −1.43959 −0.719795 0.694187i \(-0.755764\pi\)
−0.719795 + 0.694187i \(0.755764\pi\)
\(200\) 6.35448 0.449330
\(201\) 0 0
\(202\) −21.7306 −1.52896
\(203\) 2.64378 0.185557
\(204\) 0 0
\(205\) 4.00894 0.279996
\(206\) −18.7926 −1.30934
\(207\) 0 0
\(208\) 23.6010 1.63643
\(209\) 2.07191 0.143317
\(210\) 0 0
\(211\) −14.7670 −1.01660 −0.508302 0.861179i \(-0.669727\pi\)
−0.508302 + 0.861179i \(0.669727\pi\)
\(212\) −5.42748 −0.372761
\(213\) 0 0
\(214\) 10.2450 0.700334
\(215\) 15.1686 1.03449
\(216\) 0 0
\(217\) 10.1731 0.690594
\(218\) −17.1285 −1.16009
\(219\) 0 0
\(220\) −0.386638 −0.0260671
\(221\) −6.54540 −0.440291
\(222\) 0 0
\(223\) 4.22162 0.282701 0.141350 0.989960i \(-0.454856\pi\)
0.141350 + 0.989960i \(0.454856\pi\)
\(224\) −8.33694 −0.557035
\(225\) 0 0
\(226\) 26.9166 1.79046
\(227\) −13.0065 −0.863270 −0.431635 0.902048i \(-0.642063\pi\)
−0.431635 + 0.902048i \(0.642063\pi\)
\(228\) 0 0
\(229\) 6.50323 0.429745 0.214873 0.976642i \(-0.431066\pi\)
0.214873 + 0.976642i \(0.431066\pi\)
\(230\) −2.39188 −0.157716
\(231\) 0 0
\(232\) −2.28819 −0.150227
\(233\) −20.9064 −1.36963 −0.684813 0.728719i \(-0.740116\pi\)
−0.684813 + 0.728719i \(0.740116\pi\)
\(234\) 0 0
\(235\) −18.3363 −1.19613
\(236\) −3.20671 −0.208739
\(237\) 0 0
\(238\) 5.66761 0.367376
\(239\) −17.6537 −1.14192 −0.570962 0.820976i \(-0.693430\pi\)
−0.570962 + 0.820976i \(0.693430\pi\)
\(240\) 0 0
\(241\) 4.04271 0.260414 0.130207 0.991487i \(-0.458436\pi\)
0.130207 + 0.991487i \(0.458436\pi\)
\(242\) −17.3192 −1.11332
\(243\) 0 0
\(244\) −7.30494 −0.467651
\(245\) 0.0155339 0.000992425 0
\(246\) 0 0
\(247\) −22.4515 −1.42856
\(248\) −8.80479 −0.559105
\(249\) 0 0
\(250\) 18.6019 1.17649
\(251\) −19.5029 −1.23101 −0.615507 0.788132i \(-0.711049\pi\)
−0.615507 + 0.788132i \(0.711049\pi\)
\(252\) 0 0
\(253\) 0.452028 0.0284188
\(254\) −21.5501 −1.35217
\(255\) 0 0
\(256\) 12.7440 0.796499
\(257\) 5.61448 0.350222 0.175111 0.984549i \(-0.443972\pi\)
0.175111 + 0.984549i \(0.443972\pi\)
\(258\) 0 0
\(259\) 13.9408 0.866241
\(260\) 4.18966 0.259832
\(261\) 0 0
\(262\) −22.8125 −1.40936
\(263\) 6.89759 0.425324 0.212662 0.977126i \(-0.431787\pi\)
0.212662 + 0.977126i \(0.431787\pi\)
\(264\) 0 0
\(265\) 14.1054 0.866485
\(266\) 19.4406 1.19198
\(267\) 0 0
\(268\) −6.15955 −0.376254
\(269\) 20.8808 1.27313 0.636563 0.771225i \(-0.280356\pi\)
0.636563 + 0.771225i \(0.280356\pi\)
\(270\) 0 0
\(271\) 23.2030 1.40948 0.704740 0.709466i \(-0.251064\pi\)
0.704740 + 0.709466i \(0.251064\pi\)
\(272\) −6.43852 −0.390393
\(273\) 0 0
\(274\) 17.2141 1.03994
\(275\) −1.25532 −0.0756985
\(276\) 0 0
\(277\) 14.5240 0.872663 0.436331 0.899786i \(-0.356278\pi\)
0.436331 + 0.899786i \(0.356278\pi\)
\(278\) 29.1125 1.74605
\(279\) 0 0
\(280\) 9.01945 0.539015
\(281\) 24.9248 1.48689 0.743445 0.668797i \(-0.233191\pi\)
0.743445 + 0.668797i \(0.233191\pi\)
\(282\) 0 0
\(283\) −19.0099 −1.13002 −0.565010 0.825084i \(-0.691128\pi\)
−0.565010 + 0.825084i \(0.691128\pi\)
\(284\) −3.43867 −0.204048
\(285\) 0 0
\(286\) −3.55209 −0.210039
\(287\) −7.10874 −0.419616
\(288\) 0 0
\(289\) −15.2144 −0.894963
\(290\) −2.39188 −0.140456
\(291\) 0 0
\(292\) −2.75860 −0.161435
\(293\) −20.5871 −1.20271 −0.601356 0.798982i \(-0.705372\pi\)
−0.601356 + 0.798982i \(0.705372\pi\)
\(294\) 0 0
\(295\) 8.33384 0.485215
\(296\) −12.0658 −0.701309
\(297\) 0 0
\(298\) −15.3290 −0.887987
\(299\) −4.89824 −0.283273
\(300\) 0 0
\(301\) −26.8973 −1.55033
\(302\) 5.96913 0.343485
\(303\) 0 0
\(304\) −22.0849 −1.26666
\(305\) 18.9846 1.08706
\(306\) 0 0
\(307\) −27.4167 −1.56475 −0.782377 0.622805i \(-0.785993\pi\)
−0.782377 + 0.622805i \(0.785993\pi\)
\(308\) 0.685595 0.0390654
\(309\) 0 0
\(310\) −9.20380 −0.522741
\(311\) 10.1383 0.574892 0.287446 0.957797i \(-0.407194\pi\)
0.287446 + 0.957797i \(0.407194\pi\)
\(312\) 0 0
\(313\) −2.20484 −0.124625 −0.0623125 0.998057i \(-0.519848\pi\)
−0.0623125 + 0.998057i \(0.519848\pi\)
\(314\) 15.6796 0.884853
\(315\) 0 0
\(316\) −8.19408 −0.460953
\(317\) −7.39664 −0.415437 −0.207718 0.978189i \(-0.566604\pi\)
−0.207718 + 0.978189i \(0.566604\pi\)
\(318\) 0 0
\(319\) 0.452028 0.0253087
\(320\) −6.82493 −0.381525
\(321\) 0 0
\(322\) 4.24134 0.236361
\(323\) 6.12493 0.340800
\(324\) 0 0
\(325\) 13.6028 0.754547
\(326\) 16.1629 0.895180
\(327\) 0 0
\(328\) 6.15261 0.339721
\(329\) 32.5144 1.79258
\(330\) 0 0
\(331\) −12.9076 −0.709468 −0.354734 0.934967i \(-0.615429\pi\)
−0.354734 + 0.934967i \(0.615429\pi\)
\(332\) −1.42425 −0.0781659
\(333\) 0 0
\(334\) 15.6934 0.858705
\(335\) 16.0079 0.874605
\(336\) 0 0
\(337\) 4.95912 0.270141 0.135070 0.990836i \(-0.456874\pi\)
0.135070 + 0.990836i \(0.456874\pi\)
\(338\) 17.6354 0.959239
\(339\) 0 0
\(340\) −1.14297 −0.0619862
\(341\) 1.73937 0.0941922
\(342\) 0 0
\(343\) −18.5340 −1.00074
\(344\) 23.2796 1.25515
\(345\) 0 0
\(346\) −1.12245 −0.0603431
\(347\) 31.3082 1.68071 0.840357 0.542034i \(-0.182346\pi\)
0.840357 + 0.542034i \(0.182346\pi\)
\(348\) 0 0
\(349\) −3.96837 −0.212422 −0.106211 0.994344i \(-0.533872\pi\)
−0.106211 + 0.994344i \(0.533872\pi\)
\(350\) −11.7785 −0.629590
\(351\) 0 0
\(352\) −1.42543 −0.0759758
\(353\) 3.84478 0.204637 0.102318 0.994752i \(-0.467374\pi\)
0.102318 + 0.994752i \(0.467374\pi\)
\(354\) 0 0
\(355\) 8.93669 0.474310
\(356\) 1.04536 0.0554041
\(357\) 0 0
\(358\) 9.44419 0.499141
\(359\) −0.721752 −0.0380926 −0.0190463 0.999819i \(-0.506063\pi\)
−0.0190463 + 0.999819i \(0.506063\pi\)
\(360\) 0 0
\(361\) 2.00926 0.105750
\(362\) −12.9433 −0.680287
\(363\) 0 0
\(364\) −7.42920 −0.389396
\(365\) 7.16928 0.375257
\(366\) 0 0
\(367\) 23.9020 1.24768 0.623838 0.781554i \(-0.285573\pi\)
0.623838 + 0.781554i \(0.285573\pi\)
\(368\) −4.81826 −0.251169
\(369\) 0 0
\(370\) −12.6126 −0.655696
\(371\) −25.0120 −1.29856
\(372\) 0 0
\(373\) 17.5517 0.908794 0.454397 0.890799i \(-0.349855\pi\)
0.454397 + 0.890799i \(0.349855\pi\)
\(374\) 0.969035 0.0501076
\(375\) 0 0
\(376\) −28.1412 −1.45127
\(377\) −4.89824 −0.252272
\(378\) 0 0
\(379\) −24.5915 −1.26318 −0.631590 0.775303i \(-0.717597\pi\)
−0.631590 + 0.775303i \(0.717597\pi\)
\(380\) −3.92052 −0.201119
\(381\) 0 0
\(382\) −13.1588 −0.673264
\(383\) 5.49843 0.280957 0.140478 0.990084i \(-0.455136\pi\)
0.140478 + 0.990084i \(0.455136\pi\)
\(384\) 0 0
\(385\) −1.78178 −0.0908077
\(386\) 10.4079 0.529749
\(387\) 0 0
\(388\) 3.25662 0.165330
\(389\) 24.3699 1.23561 0.617803 0.786333i \(-0.288023\pi\)
0.617803 + 0.786333i \(0.288023\pi\)
\(390\) 0 0
\(391\) 1.33628 0.0675784
\(392\) 0.0238402 0.00120411
\(393\) 0 0
\(394\) −6.91816 −0.348532
\(395\) 21.2954 1.07149
\(396\) 0 0
\(397\) −24.1489 −1.21200 −0.606000 0.795464i \(-0.707227\pi\)
−0.606000 + 0.795464i \(0.707227\pi\)
\(398\) −32.5794 −1.63306
\(399\) 0 0
\(400\) 13.3807 0.669034
\(401\) −32.4595 −1.62095 −0.810475 0.585774i \(-0.800791\pi\)
−0.810475 + 0.585774i \(0.800791\pi\)
\(402\) 0 0
\(403\) −18.8481 −0.938889
\(404\) −7.77088 −0.386616
\(405\) 0 0
\(406\) 4.24134 0.210494
\(407\) 2.38357 0.118149
\(408\) 0 0
\(409\) 19.6683 0.972534 0.486267 0.873810i \(-0.338358\pi\)
0.486267 + 0.873810i \(0.338358\pi\)
\(410\) 6.43142 0.317625
\(411\) 0 0
\(412\) −6.72025 −0.331083
\(413\) −14.7778 −0.727166
\(414\) 0 0
\(415\) 3.70145 0.181697
\(416\) 15.4462 0.757312
\(417\) 0 0
\(418\) 3.32391 0.162578
\(419\) −27.2402 −1.33077 −0.665385 0.746501i \(-0.731732\pi\)
−0.665385 + 0.746501i \(0.731732\pi\)
\(420\) 0 0
\(421\) 4.89033 0.238340 0.119170 0.992874i \(-0.461977\pi\)
0.119170 + 0.992874i \(0.461977\pi\)
\(422\) −23.6903 −1.15323
\(423\) 0 0
\(424\) 21.6478 1.05131
\(425\) −3.71094 −0.180007
\(426\) 0 0
\(427\) −33.6640 −1.62911
\(428\) 3.66362 0.177088
\(429\) 0 0
\(430\) 24.3345 1.17352
\(431\) 19.6984 0.948838 0.474419 0.880299i \(-0.342658\pi\)
0.474419 + 0.880299i \(0.342658\pi\)
\(432\) 0 0
\(433\) 10.5432 0.506672 0.253336 0.967378i \(-0.418472\pi\)
0.253336 + 0.967378i \(0.418472\pi\)
\(434\) 16.3204 0.783404
\(435\) 0 0
\(436\) −6.12515 −0.293342
\(437\) 4.58359 0.219263
\(438\) 0 0
\(439\) −22.3066 −1.06464 −0.532319 0.846544i \(-0.678679\pi\)
−0.532319 + 0.846544i \(0.678679\pi\)
\(440\) 1.54213 0.0735180
\(441\) 0 0
\(442\) −10.5006 −0.499463
\(443\) 36.5774 1.73785 0.868923 0.494947i \(-0.164813\pi\)
0.868923 + 0.494947i \(0.164813\pi\)
\(444\) 0 0
\(445\) −2.71677 −0.128787
\(446\) 6.77263 0.320693
\(447\) 0 0
\(448\) 12.1021 0.571772
\(449\) −11.7639 −0.555172 −0.277586 0.960701i \(-0.589534\pi\)
−0.277586 + 0.960701i \(0.589534\pi\)
\(450\) 0 0
\(451\) −1.21544 −0.0572327
\(452\) 9.62539 0.452740
\(453\) 0 0
\(454\) −20.8659 −0.979286
\(455\) 19.3076 0.905153
\(456\) 0 0
\(457\) −2.47480 −0.115766 −0.0578832 0.998323i \(-0.518435\pi\)
−0.0578832 + 0.998323i \(0.518435\pi\)
\(458\) 10.4329 0.487499
\(459\) 0 0
\(460\) −0.855340 −0.0398804
\(461\) 32.6980 1.52290 0.761449 0.648225i \(-0.224489\pi\)
0.761449 + 0.648225i \(0.224489\pi\)
\(462\) 0 0
\(463\) −11.8696 −0.551628 −0.275814 0.961211i \(-0.588947\pi\)
−0.275814 + 0.961211i \(0.588947\pi\)
\(464\) −4.81826 −0.223682
\(465\) 0 0
\(466\) −33.5396 −1.55369
\(467\) 2.70620 0.125228 0.0626141 0.998038i \(-0.480056\pi\)
0.0626141 + 0.998038i \(0.480056\pi\)
\(468\) 0 0
\(469\) −28.3856 −1.31072
\(470\) −29.4165 −1.35688
\(471\) 0 0
\(472\) 12.7901 0.588714
\(473\) −4.59884 −0.211455
\(474\) 0 0
\(475\) −12.7290 −0.584045
\(476\) 2.02674 0.0928955
\(477\) 0 0
\(478\) −28.3214 −1.29539
\(479\) 8.28008 0.378327 0.189163 0.981946i \(-0.439422\pi\)
0.189163 + 0.981946i \(0.439422\pi\)
\(480\) 0 0
\(481\) −25.8287 −1.17769
\(482\) 6.48561 0.295412
\(483\) 0 0
\(484\) −6.19336 −0.281516
\(485\) −8.46355 −0.384310
\(486\) 0 0
\(487\) −23.3641 −1.05873 −0.529363 0.848395i \(-0.677569\pi\)
−0.529363 + 0.848395i \(0.677569\pi\)
\(488\) 29.1362 1.31893
\(489\) 0 0
\(490\) 0.0249206 0.00112580
\(491\) 27.8118 1.25513 0.627565 0.778564i \(-0.284052\pi\)
0.627565 + 0.778564i \(0.284052\pi\)
\(492\) 0 0
\(493\) 1.33628 0.0601828
\(494\) −36.0183 −1.62054
\(495\) 0 0
\(496\) −18.5403 −0.832484
\(497\) −15.8467 −0.710824
\(498\) 0 0
\(499\) 2.79228 0.124999 0.0624997 0.998045i \(-0.480093\pi\)
0.0624997 + 0.998045i \(0.480093\pi\)
\(500\) 6.65204 0.297488
\(501\) 0 0
\(502\) −31.2880 −1.39645
\(503\) −14.7701 −0.658567 −0.329283 0.944231i \(-0.606807\pi\)
−0.329283 + 0.944231i \(0.606807\pi\)
\(504\) 0 0
\(505\) 20.1956 0.898691
\(506\) 0.725176 0.0322380
\(507\) 0 0
\(508\) −7.70633 −0.341913
\(509\) −18.7434 −0.830786 −0.415393 0.909642i \(-0.636356\pi\)
−0.415393 + 0.909642i \(0.636356\pi\)
\(510\) 0 0
\(511\) −12.7127 −0.562378
\(512\) −6.85622 −0.303005
\(513\) 0 0
\(514\) 9.00716 0.397289
\(515\) 17.4651 0.769604
\(516\) 0 0
\(517\) 5.55924 0.244495
\(518\) 22.3649 0.982657
\(519\) 0 0
\(520\) −16.7107 −0.732813
\(521\) 5.71918 0.250562 0.125281 0.992121i \(-0.460017\pi\)
0.125281 + 0.992121i \(0.460017\pi\)
\(522\) 0 0
\(523\) −23.2442 −1.01640 −0.508199 0.861240i \(-0.669689\pi\)
−0.508199 + 0.861240i \(0.669689\pi\)
\(524\) −8.15775 −0.356373
\(525\) 0 0
\(526\) 11.0656 0.482484
\(527\) 5.14189 0.223984
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 22.6288 0.982934
\(531\) 0 0
\(532\) 6.95196 0.301406
\(533\) 13.1706 0.570484
\(534\) 0 0
\(535\) −9.52130 −0.411642
\(536\) 24.5677 1.06116
\(537\) 0 0
\(538\) 33.4985 1.44422
\(539\) −0.00470960 −0.000202857 0
\(540\) 0 0
\(541\) 37.5964 1.61640 0.808198 0.588911i \(-0.200443\pi\)
0.808198 + 0.588911i \(0.200443\pi\)
\(542\) 37.2239 1.59890
\(543\) 0 0
\(544\) −4.21383 −0.180667
\(545\) 15.9185 0.681874
\(546\) 0 0
\(547\) 38.5226 1.64711 0.823554 0.567237i \(-0.191988\pi\)
0.823554 + 0.567237i \(0.191988\pi\)
\(548\) 6.15577 0.262962
\(549\) 0 0
\(550\) −2.01387 −0.0858717
\(551\) 4.58359 0.195267
\(552\) 0 0
\(553\) −37.7615 −1.60578
\(554\) 23.3005 0.989941
\(555\) 0 0
\(556\) 10.4106 0.441510
\(557\) −2.46258 −0.104343 −0.0521715 0.998638i \(-0.516614\pi\)
−0.0521715 + 0.998638i \(0.516614\pi\)
\(558\) 0 0
\(559\) 49.8337 2.10774
\(560\) 18.9923 0.802572
\(561\) 0 0
\(562\) 39.9862 1.68672
\(563\) −40.2244 −1.69525 −0.847627 0.530592i \(-0.821970\pi\)
−0.847627 + 0.530592i \(0.821970\pi\)
\(564\) 0 0
\(565\) −25.0152 −1.05240
\(566\) −30.4970 −1.28189
\(567\) 0 0
\(568\) 13.7153 0.575483
\(569\) 28.8951 1.21134 0.605672 0.795714i \(-0.292904\pi\)
0.605672 + 0.795714i \(0.292904\pi\)
\(570\) 0 0
\(571\) −9.67958 −0.405078 −0.202539 0.979274i \(-0.564919\pi\)
−0.202539 + 0.979274i \(0.564919\pi\)
\(572\) −1.27023 −0.0531109
\(573\) 0 0
\(574\) −11.4044 −0.476008
\(575\) −2.77708 −0.115812
\(576\) 0 0
\(577\) −4.84531 −0.201713 −0.100856 0.994901i \(-0.532158\pi\)
−0.100856 + 0.994901i \(0.532158\pi\)
\(578\) −24.4080 −1.01524
\(579\) 0 0
\(580\) −0.855340 −0.0355160
\(581\) −6.56350 −0.272300
\(582\) 0 0
\(583\) −4.27649 −0.177114
\(584\) 11.0029 0.455301
\(585\) 0 0
\(586\) −33.0273 −1.36435
\(587\) 38.9485 1.60758 0.803788 0.594916i \(-0.202815\pi\)
0.803788 + 0.594916i \(0.202815\pi\)
\(588\) 0 0
\(589\) 17.6373 0.726732
\(590\) 13.3697 0.550424
\(591\) 0 0
\(592\) −25.4070 −1.04422
\(593\) −7.84842 −0.322296 −0.161148 0.986930i \(-0.551520\pi\)
−0.161148 + 0.986930i \(0.551520\pi\)
\(594\) 0 0
\(595\) −5.26725 −0.215936
\(596\) −5.48167 −0.224538
\(597\) 0 0
\(598\) −7.85811 −0.321342
\(599\) 20.9165 0.854626 0.427313 0.904104i \(-0.359460\pi\)
0.427313 + 0.904104i \(0.359460\pi\)
\(600\) 0 0
\(601\) 5.37909 0.219418 0.109709 0.993964i \(-0.465008\pi\)
0.109709 + 0.993964i \(0.465008\pi\)
\(602\) −43.1506 −1.75869
\(603\) 0 0
\(604\) 2.13456 0.0868542
\(605\) 16.0958 0.654386
\(606\) 0 0
\(607\) 34.3675 1.39493 0.697467 0.716617i \(-0.254310\pi\)
0.697467 + 0.716617i \(0.254310\pi\)
\(608\) −14.4540 −0.586185
\(609\) 0 0
\(610\) 30.4565 1.23315
\(611\) −60.2407 −2.43708
\(612\) 0 0
\(613\) −33.6862 −1.36057 −0.680286 0.732947i \(-0.738144\pi\)
−0.680286 + 0.732947i \(0.738144\pi\)
\(614\) −43.9839 −1.77504
\(615\) 0 0
\(616\) −2.73453 −0.110178
\(617\) −9.80268 −0.394641 −0.197320 0.980339i \(-0.563224\pi\)
−0.197320 + 0.980339i \(0.563224\pi\)
\(618\) 0 0
\(619\) 14.2483 0.572688 0.286344 0.958127i \(-0.407560\pi\)
0.286344 + 0.958127i \(0.407560\pi\)
\(620\) −3.29128 −0.132181
\(621\) 0 0
\(622\) 16.2646 0.652153
\(623\) 4.81744 0.193007
\(624\) 0 0
\(625\) −3.40245 −0.136098
\(626\) −3.53717 −0.141374
\(627\) 0 0
\(628\) 5.60705 0.223746
\(629\) 7.04627 0.280953
\(630\) 0 0
\(631\) 8.76698 0.349008 0.174504 0.984656i \(-0.444168\pi\)
0.174504 + 0.984656i \(0.444168\pi\)
\(632\) 32.6826 1.30004
\(633\) 0 0
\(634\) −11.8662 −0.471268
\(635\) 20.0278 0.794779
\(636\) 0 0
\(637\) 0.0510339 0.00202204
\(638\) 0.725176 0.0287100
\(639\) 0 0
\(640\) −20.3522 −0.804491
\(641\) 33.6529 1.32921 0.664605 0.747195i \(-0.268600\pi\)
0.664605 + 0.747195i \(0.268600\pi\)
\(642\) 0 0
\(643\) −17.7464 −0.699851 −0.349926 0.936777i \(-0.613793\pi\)
−0.349926 + 0.936777i \(0.613793\pi\)
\(644\) 1.51671 0.0597667
\(645\) 0 0
\(646\) 9.82606 0.386601
\(647\) −13.9050 −0.546663 −0.273332 0.961920i \(-0.588126\pi\)
−0.273332 + 0.961920i \(0.588126\pi\)
\(648\) 0 0
\(649\) −2.52667 −0.0991805
\(650\) 21.8226 0.855952
\(651\) 0 0
\(652\) 5.77986 0.226357
\(653\) −20.1732 −0.789440 −0.394720 0.918801i \(-0.629158\pi\)
−0.394720 + 0.918801i \(0.629158\pi\)
\(654\) 0 0
\(655\) 21.2010 0.828392
\(656\) 12.9556 0.505831
\(657\) 0 0
\(658\) 52.1619 2.03348
\(659\) 46.8861 1.82642 0.913212 0.407485i \(-0.133594\pi\)
0.913212 + 0.407485i \(0.133594\pi\)
\(660\) 0 0
\(661\) −47.0205 −1.82888 −0.914442 0.404716i \(-0.867370\pi\)
−0.914442 + 0.404716i \(0.867370\pi\)
\(662\) −20.7074 −0.804815
\(663\) 0 0
\(664\) 5.68070 0.220454
\(665\) −18.0673 −0.700620
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 5.61198 0.217134
\(669\) 0 0
\(670\) 25.6810 0.992145
\(671\) −5.75580 −0.222200
\(672\) 0 0
\(673\) 25.5133 0.983466 0.491733 0.870746i \(-0.336364\pi\)
0.491733 + 0.870746i \(0.336364\pi\)
\(674\) 7.95578 0.306445
\(675\) 0 0
\(676\) 6.30643 0.242555
\(677\) 45.7948 1.76004 0.880019 0.474939i \(-0.157530\pi\)
0.880019 + 0.474939i \(0.157530\pi\)
\(678\) 0 0
\(679\) 15.0078 0.575945
\(680\) 4.55880 0.174822
\(681\) 0 0
\(682\) 2.79043 0.106851
\(683\) −29.2313 −1.11850 −0.559252 0.828998i \(-0.688911\pi\)
−0.559252 + 0.828998i \(0.688911\pi\)
\(684\) 0 0
\(685\) −15.9981 −0.611256
\(686\) −29.7336 −1.13523
\(687\) 0 0
\(688\) 49.0200 1.86887
\(689\) 46.3407 1.76544
\(690\) 0 0
\(691\) −13.4405 −0.511302 −0.255651 0.966769i \(-0.582290\pi\)
−0.255651 + 0.966769i \(0.582290\pi\)
\(692\) −0.401388 −0.0152585
\(693\) 0 0
\(694\) 50.2269 1.90659
\(695\) −27.0560 −1.02629
\(696\) 0 0
\(697\) −3.59305 −0.136096
\(698\) −6.36634 −0.240969
\(699\) 0 0
\(700\) −4.21202 −0.159199
\(701\) −34.4809 −1.30233 −0.651164 0.758937i \(-0.725719\pi\)
−0.651164 + 0.758937i \(0.725719\pi\)
\(702\) 0 0
\(703\) 24.1695 0.911572
\(704\) 2.06920 0.0779857
\(705\) 0 0
\(706\) 6.16807 0.232138
\(707\) −35.8113 −1.34682
\(708\) 0 0
\(709\) −2.67200 −0.100349 −0.0501746 0.998740i \(-0.515978\pi\)
−0.0501746 + 0.998740i \(0.515978\pi\)
\(710\) 14.3369 0.538054
\(711\) 0 0
\(712\) −4.16949 −0.156258
\(713\) 3.84793 0.144106
\(714\) 0 0
\(715\) 3.30117 0.123457
\(716\) 3.37725 0.126214
\(717\) 0 0
\(718\) −1.15789 −0.0432119
\(719\) −2.13450 −0.0796034 −0.0398017 0.999208i \(-0.512673\pi\)
−0.0398017 + 0.999208i \(0.512673\pi\)
\(720\) 0 0
\(721\) −30.9695 −1.15336
\(722\) 3.22339 0.119962
\(723\) 0 0
\(724\) −4.62855 −0.172019
\(725\) −2.77708 −0.103138
\(726\) 0 0
\(727\) 29.8021 1.10530 0.552650 0.833414i \(-0.313617\pi\)
0.552650 + 0.833414i \(0.313617\pi\)
\(728\) 29.6318 1.09823
\(729\) 0 0
\(730\) 11.5015 0.425688
\(731\) −13.5950 −0.502829
\(732\) 0 0
\(733\) 21.7312 0.802660 0.401330 0.915934i \(-0.368548\pi\)
0.401330 + 0.915934i \(0.368548\pi\)
\(734\) 38.3453 1.41535
\(735\) 0 0
\(736\) −3.15342 −0.116236
\(737\) −4.85331 −0.178774
\(738\) 0 0
\(739\) −0.292924 −0.0107754 −0.00538769 0.999985i \(-0.501715\pi\)
−0.00538769 + 0.999985i \(0.501715\pi\)
\(740\) −4.51026 −0.165801
\(741\) 0 0
\(742\) −40.1260 −1.47307
\(743\) 37.9029 1.39052 0.695261 0.718757i \(-0.255289\pi\)
0.695261 + 0.718757i \(0.255289\pi\)
\(744\) 0 0
\(745\) 14.2462 0.521940
\(746\) 28.1578 1.03093
\(747\) 0 0
\(748\) 0.346528 0.0126703
\(749\) 16.8834 0.616906
\(750\) 0 0
\(751\) 37.0898 1.35343 0.676713 0.736247i \(-0.263404\pi\)
0.676713 + 0.736247i \(0.263404\pi\)
\(752\) −59.2571 −2.16088
\(753\) 0 0
\(754\) −7.85811 −0.286176
\(755\) −5.54747 −0.201893
\(756\) 0 0
\(757\) 14.6336 0.531867 0.265934 0.963991i \(-0.414320\pi\)
0.265934 + 0.963991i \(0.414320\pi\)
\(758\) −39.4514 −1.43294
\(759\) 0 0
\(760\) 15.6372 0.567222
\(761\) 15.1704 0.549926 0.274963 0.961455i \(-0.411334\pi\)
0.274963 + 0.961455i \(0.411334\pi\)
\(762\) 0 0
\(763\) −28.2271 −1.02189
\(764\) −4.70561 −0.170243
\(765\) 0 0
\(766\) 8.82098 0.318715
\(767\) 27.3794 0.988611
\(768\) 0 0
\(769\) 34.0412 1.22756 0.613779 0.789478i \(-0.289649\pi\)
0.613779 + 0.789478i \(0.289649\pi\)
\(770\) −2.85845 −0.103012
\(771\) 0 0
\(772\) 3.72188 0.133953
\(773\) 26.8567 0.965967 0.482983 0.875630i \(-0.339553\pi\)
0.482983 + 0.875630i \(0.339553\pi\)
\(774\) 0 0
\(775\) −10.6860 −0.383852
\(776\) −12.9892 −0.466285
\(777\) 0 0
\(778\) 39.0960 1.40166
\(779\) −12.3246 −0.441574
\(780\) 0 0
\(781\) −2.70944 −0.0969515
\(782\) 2.14375 0.0766603
\(783\) 0 0
\(784\) 0.0502006 0.00179288
\(785\) −14.5720 −0.520098
\(786\) 0 0
\(787\) −28.3930 −1.01210 −0.506050 0.862504i \(-0.668895\pi\)
−0.506050 + 0.862504i \(0.668895\pi\)
\(788\) −2.47394 −0.0881305
\(789\) 0 0
\(790\) 34.1636 1.21549
\(791\) 44.3576 1.57717
\(792\) 0 0
\(793\) 62.3706 2.21485
\(794\) −38.7415 −1.37488
\(795\) 0 0
\(796\) −11.6504 −0.412938
\(797\) 23.8372 0.844358 0.422179 0.906513i \(-0.361265\pi\)
0.422179 + 0.906513i \(0.361265\pi\)
\(798\) 0 0
\(799\) 16.4341 0.581397
\(800\) 8.75728 0.309617
\(801\) 0 0
\(802\) −52.0738 −1.83879
\(803\) −2.17359 −0.0767045
\(804\) 0 0
\(805\) −3.94174 −0.138928
\(806\) −30.2374 −1.06507
\(807\) 0 0
\(808\) 30.9946 1.09039
\(809\) 15.5078 0.545224 0.272612 0.962124i \(-0.412113\pi\)
0.272612 + 0.962124i \(0.412113\pi\)
\(810\) 0 0
\(811\) 10.1480 0.356345 0.178173 0.983999i \(-0.442981\pi\)
0.178173 + 0.983999i \(0.442981\pi\)
\(812\) 1.51671 0.0532260
\(813\) 0 0
\(814\) 3.82390 0.134028
\(815\) −15.0212 −0.526168
\(816\) 0 0
\(817\) −46.6325 −1.63146
\(818\) 31.5533 1.10323
\(819\) 0 0
\(820\) 2.29988 0.0803154
\(821\) 41.5099 1.44870 0.724352 0.689430i \(-0.242139\pi\)
0.724352 + 0.689430i \(0.242139\pi\)
\(822\) 0 0
\(823\) −32.8195 −1.14402 −0.572008 0.820248i \(-0.693835\pi\)
−0.572008 + 0.820248i \(0.693835\pi\)
\(824\) 26.8041 0.933765
\(825\) 0 0
\(826\) −23.7075 −0.824891
\(827\) −26.0045 −0.904264 −0.452132 0.891951i \(-0.649336\pi\)
−0.452132 + 0.891951i \(0.649336\pi\)
\(828\) 0 0
\(829\) 49.0052 1.70202 0.851010 0.525150i \(-0.175991\pi\)
0.851010 + 0.525150i \(0.175991\pi\)
\(830\) 5.93814 0.206116
\(831\) 0 0
\(832\) −22.4221 −0.777346
\(833\) −0.0139224 −0.000482383 0
\(834\) 0 0
\(835\) −14.5848 −0.504729
\(836\) 1.18863 0.0411097
\(837\) 0 0
\(838\) −43.7006 −1.50961
\(839\) −10.6093 −0.366273 −0.183137 0.983087i \(-0.558625\pi\)
−0.183137 + 0.983087i \(0.558625\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 7.84542 0.270371
\(843\) 0 0
\(844\) −8.47168 −0.291607
\(845\) −16.3896 −0.563820
\(846\) 0 0
\(847\) −28.5414 −0.980694
\(848\) 45.5840 1.56536
\(849\) 0 0
\(850\) −5.95336 −0.204199
\(851\) 5.27307 0.180758
\(852\) 0 0
\(853\) −44.0684 −1.50887 −0.754436 0.656374i \(-0.772089\pi\)
−0.754436 + 0.656374i \(0.772089\pi\)
\(854\) −54.0062 −1.84805
\(855\) 0 0
\(856\) −14.6126 −0.499447
\(857\) 26.3167 0.898961 0.449480 0.893290i \(-0.351609\pi\)
0.449480 + 0.893290i \(0.351609\pi\)
\(858\) 0 0
\(859\) 7.80205 0.266202 0.133101 0.991102i \(-0.457506\pi\)
0.133101 + 0.991102i \(0.457506\pi\)
\(860\) 8.70205 0.296737
\(861\) 0 0
\(862\) 31.6016 1.07635
\(863\) −4.04966 −0.137852 −0.0689260 0.997622i \(-0.521957\pi\)
−0.0689260 + 0.997622i \(0.521957\pi\)
\(864\) 0 0
\(865\) 1.04316 0.0354684
\(866\) 16.9141 0.574764
\(867\) 0 0
\(868\) 5.83618 0.198093
\(869\) −6.45639 −0.219018
\(870\) 0 0
\(871\) 52.5911 1.78198
\(872\) 24.4305 0.827322
\(873\) 0 0
\(874\) 7.35332 0.248730
\(875\) 30.6552 1.03633
\(876\) 0 0
\(877\) −48.5571 −1.63966 −0.819828 0.572610i \(-0.805931\pi\)
−0.819828 + 0.572610i \(0.805931\pi\)
\(878\) −35.7859 −1.20772
\(879\) 0 0
\(880\) 3.24727 0.109465
\(881\) −29.7511 −1.00234 −0.501170 0.865349i \(-0.667097\pi\)
−0.501170 + 0.865349i \(0.667097\pi\)
\(882\) 0 0
\(883\) −38.6702 −1.30136 −0.650678 0.759353i \(-0.725515\pi\)
−0.650678 + 0.759353i \(0.725515\pi\)
\(884\) −3.75502 −0.126295
\(885\) 0 0
\(886\) 58.6802 1.97140
\(887\) 19.8178 0.665417 0.332709 0.943030i \(-0.392037\pi\)
0.332709 + 0.943030i \(0.392037\pi\)
\(888\) 0 0
\(889\) −35.5138 −1.19109
\(890\) −4.35844 −0.146095
\(891\) 0 0
\(892\) 2.42190 0.0810911
\(893\) 56.3710 1.88638
\(894\) 0 0
\(895\) −8.77705 −0.293385
\(896\) 36.0890 1.20565
\(897\) 0 0
\(898\) −18.8725 −0.629783
\(899\) 3.84793 0.128336
\(900\) 0 0
\(901\) −12.6421 −0.421168
\(902\) −1.94989 −0.0649243
\(903\) 0 0
\(904\) −38.3914 −1.27688
\(905\) 12.0290 0.399859
\(906\) 0 0
\(907\) 43.5513 1.44610 0.723048 0.690798i \(-0.242741\pi\)
0.723048 + 0.690798i \(0.242741\pi\)
\(908\) −7.46167 −0.247624
\(909\) 0 0
\(910\) 30.9746 1.02680
\(911\) −18.3499 −0.607958 −0.303979 0.952679i \(-0.598315\pi\)
−0.303979 + 0.952679i \(0.598315\pi\)
\(912\) 0 0
\(913\) −1.12221 −0.0371398
\(914\) −3.97026 −0.131325
\(915\) 0 0
\(916\) 3.73083 0.123270
\(917\) −37.5941 −1.24147
\(918\) 0 0
\(919\) 18.0400 0.595084 0.297542 0.954709i \(-0.403833\pi\)
0.297542 + 0.954709i \(0.403833\pi\)
\(920\) 3.41157 0.112476
\(921\) 0 0
\(922\) 52.4565 1.72756
\(923\) 29.3599 0.966393
\(924\) 0 0
\(925\) −14.6437 −0.481482
\(926\) −19.0421 −0.625762
\(927\) 0 0
\(928\) −3.15342 −0.103516
\(929\) −8.78537 −0.288239 −0.144119 0.989560i \(-0.546035\pi\)
−0.144119 + 0.989560i \(0.546035\pi\)
\(930\) 0 0
\(931\) −0.0477555 −0.00156512
\(932\) −11.9938 −0.392869
\(933\) 0 0
\(934\) 4.34149 0.142058
\(935\) −0.900583 −0.0294522
\(936\) 0 0
\(937\) −11.6752 −0.381411 −0.190706 0.981647i \(-0.561078\pi\)
−0.190706 + 0.981647i \(0.561078\pi\)
\(938\) −45.5382 −1.48687
\(939\) 0 0
\(940\) −10.5193 −0.343103
\(941\) 7.98863 0.260422 0.130211 0.991486i \(-0.458435\pi\)
0.130211 + 0.991486i \(0.458435\pi\)
\(942\) 0 0
\(943\) −2.68885 −0.0875611
\(944\) 26.9323 0.876571
\(945\) 0 0
\(946\) −7.37779 −0.239873
\(947\) −24.1149 −0.783628 −0.391814 0.920044i \(-0.628152\pi\)
−0.391814 + 0.920044i \(0.628152\pi\)
\(948\) 0 0
\(949\) 23.5534 0.764575
\(950\) −20.4207 −0.662536
\(951\) 0 0
\(952\) −8.08377 −0.261996
\(953\) 31.7749 1.02929 0.514645 0.857404i \(-0.327924\pi\)
0.514645 + 0.857404i \(0.327924\pi\)
\(954\) 0 0
\(955\) 12.2293 0.395731
\(956\) −10.1277 −0.327555
\(957\) 0 0
\(958\) 13.2835 0.429171
\(959\) 28.3682 0.916057
\(960\) 0 0
\(961\) −16.1935 −0.522370
\(962\) −41.4363 −1.33596
\(963\) 0 0
\(964\) 2.31926 0.0746983
\(965\) −9.67270 −0.311375
\(966\) 0 0
\(967\) −35.4212 −1.13907 −0.569535 0.821967i \(-0.692877\pi\)
−0.569535 + 0.821967i \(0.692877\pi\)
\(968\) 24.7026 0.793970
\(969\) 0 0
\(970\) −13.5778 −0.435958
\(971\) −29.7556 −0.954904 −0.477452 0.878658i \(-0.658440\pi\)
−0.477452 + 0.878658i \(0.658440\pi\)
\(972\) 0 0
\(973\) 47.9763 1.53805
\(974\) −37.4823 −1.20101
\(975\) 0 0
\(976\) 61.3522 1.96384
\(977\) 23.6394 0.756290 0.378145 0.925746i \(-0.376562\pi\)
0.378145 + 0.925746i \(0.376562\pi\)
\(978\) 0 0
\(979\) 0.823675 0.0263248
\(980\) 0.00891163 0.000284672 0
\(981\) 0 0
\(982\) 44.6177 1.42381
\(983\) −38.8234 −1.23827 −0.619137 0.785283i \(-0.712517\pi\)
−0.619137 + 0.785283i \(0.712517\pi\)
\(984\) 0 0
\(985\) 6.42947 0.204860
\(986\) 2.14375 0.0682709
\(987\) 0 0
\(988\) −12.8802 −0.409773
\(989\) −10.1738 −0.323508
\(990\) 0 0
\(991\) 38.4439 1.22121 0.610605 0.791935i \(-0.290926\pi\)
0.610605 + 0.791935i \(0.290926\pi\)
\(992\) −12.1341 −0.385258
\(993\) 0 0
\(994\) −25.4225 −0.806352
\(995\) 30.2780 0.959878
\(996\) 0 0
\(997\) 22.2531 0.704761 0.352381 0.935857i \(-0.385372\pi\)
0.352381 + 0.935857i \(0.385372\pi\)
\(998\) 4.47957 0.141798
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))